Analysis of spectral approximations using prolate spheroidal wave functions

Wang, Li-Lian

doi:10.1090/S0025-5718-09-02268-6

Analysis of spectral approximations using prolate spheroidal wave functions
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Math. Comp. 79 (2010), 807-827 Request permission

Abstract:

In this paper, the approximation properties of the prolate spheroidal wave functions of order zero (PSWFs) are studied, and a set of optimal error estimates are derived for the PSWF approximation of non-periodic functions in Sobolev spaces. These results serve as an indispensable tool for the analysis of PSWF spectral methods. A PSWF spectral-Galerkin method is proposed and analyzed for elliptic-type equations. Illustrative numerical results consistent with the theoretical analysis are also presented.

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